Problem: Solve for $x$ and $y$ using substitution. ${6x+4y = -10}$ ${y = -5x+1}$
Answer: Since $y$ has already been solved for, substitute $-5x+1$ for $y$ in the first equation. ${6x + 4}{(-5x+1)}{= -10}$ Simplify and solve for $x$ $6x-20x + 4 = -10$ $-14x+4 = -10$ $-14x+4{-4} = -10{-4}$ $-14x = -14$ $\dfrac{-14x}{{-14}} = \dfrac{-14}{{-14}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -5x+1}\thinspace$ to find $y$ ${y = -5}{(1)}{ + 1}$ $y = -5 + 1$ $y = -4$ You can also plug ${x = 1}$ into $\thinspace {6x+4y = -10}\thinspace$ and get the same answer for $y$ : ${6}{(1)}{ + 4y = -10}$ ${y = -4}$